To calculate the mean deviation about the mean and its coefficient, we follow these steps:

Step 1: Calculate the Mean (Arithmetic Mean)

The mean is given by: $\text{Mean} = \frac{\sum x_i}{n}$ where $x_i$ are the values of the data, and $n$ is the number of values.

For the numbers 4, 5, 6, 8, and 3: $\text{Mean} = \frac{4 + 5 + 6 + 8 + 3}{5} = \frac{26}{5} = 5.2$

Step 2: Calculate the Mean Deviation about the Mean

The mean deviation about the mean is calculated using the formula: $\text{Mean Deviation} = \frac{\sum |x_i - \text{Mean}|}{n}$ We now calculate the absolute deviations:

• $|4 - 5.2| = 1.2$
• $|5 - 5.2| = 0.2$
• $|6 - 5.2| = 0.8$
• $|8 - 5.2| = 2.8$
• $|3 - 5.2| = 2.2$

Now, sum these absolute deviations: $\sum |x_i - \text{Mean}| = 1.2 + 0.2 + 0.8 + 2.8 + 2.2 = 7.2$

Thus, the mean deviation is: $\text{Mean Deviation} = \frac{7.2}{5} = 1.44$

Step 3: Calculate the Coefficient of Mean Deviation

The coefficient of mean deviation is given by: $\text{Coefficient of Mean Deviation} = \frac{\text{Mean Deviation}}{\text{Mean}} \times 100$ Substituting the values: $\text{Coefficient of Mean Deviation} = \frac{1.44}{5.2} \times 100 \approx 27.69\%$

Final Answer:

• Mean Deviation about the Mean = 1.44
• Coefficient of Mean Deviation = 27.69%

Would you like further clarification or additional examples on this topic?

5 Related Questions:

1. How do you calculate the median deviation about the median?
2. What is the difference between mean deviation and standard deviation?
3. How does the mean deviation differ when using the median instead of the mean?
4. Can you calculate the variance for the given data set?
5. What are the applications of mean deviation in real-world scenarios?

Tip: Mean deviation is useful for understanding the average spread of data values around a central point, especially when you want to avoid squaring deviations like in variance.